This book introduces the peridynamic (PD) differential operator, which enables the nonlocal form of local differentiation. PD is a bridge between differentiation and integration. It provides the computational solution of complex field equations and evaluation of derivatives of smooth or scattered data in the presence of discontinuities. PD also serves as a natural filter to smooth noisy data and to recover missing data.

This book starts with an overview of the PD concept, the derivation of the PD differential operator, its numerical implementation for the spatial and temporal derivatives, and the description of sources of error. The applications concern interpolation, regression, and smoothing of data, solutions to nonlinear ordinary differential equations, single- and multi-field partial differential equations and integro-differential equations. It describes the derivation of the weak form of PD Poisson's and Navier's equationsfor direct imposition of essential and natural boundary conditions. It also presents an alternative approach for the PD differential operator based on the least squares minimization.

Peridynamic Differential Operator for Numerical Analysis is suitable for both advanced-level student and researchers, demonstrating how to construct solutions to all of the applications. Provided as supplementary material, solution algorithms for a set of selected applications are available for more details in the numerical implementation.

Autorentext

ERDOGAN MADENCI Erdogan Madenci is a professor in the Department of Aerospace and Mechanical Engineering at the University of Arizona. He received his B.S. degrees on both mechanical and industrial engineering, and his M.S. degree in applied mechanics from Lehigh University, Bethlehem, Pa in 1980, 1981, and 1982, respectively. He received his Ph.D. degree in engineering mechanics from the UCLA in 1987. Prior to joining the University of Arizona, he worked at Northrop Corporation, Aerospace Corporation, and Fraunhofer Institute. Also, he worked at the KTH Royal Institute of Technology, NASA Langley Research Center, Sandia National Labs and MIT as part of his sabbatical leaves. He is the lead author of three books on Peridynamic Theory and Its Applications, The Finite Element Method Using ANSYS, and Fatigue Life Prediction of Solder Joints. Recently, he started the Journal of Peridynamics and Nonlocal Modeling as the Co-Editor-in-Chief. He is a Fellow of ASME and an Associate Fellow of AIAA.

ATILA BARUT Atila Barut is a Research Associate Professor in the Department of Aerospace and Mechanical Engineering at the University of Arizona. He received his B.S. and M.S. degrees in Engineering Sciences in 1988 and 1990, respectively, from the Middle East Technical University, Turkey. He received his Ph.D. degree in Mechanical Engineering from the University of Arizona in 1998. Dr. Barut is an expert on the broad area of analytical and computational modeling of solid mechanics. Particularly, his research focused on the development of new finite elements for the analysis of composite plates and shells, and the peridynamic differential operator and its applications. He serves on the editorial board of the Journal of Peridynamics and Nonlocal Modeling.

MEHMET DORDUNCU

Mehmet Dorduncu is a Postdoctoral Researcher in the Department of Aerospace and Mechanical Engineering at the University of Arizona. He received his B.S. and M.S. degrees in Mechanical Engineering in 2011 and 2013, respectively, from Erciyas University, Turkey. He received his Ph.D. degree in Mechanical Engineering from the University of Arizona in 2018. His research has focused on the advancement of the peridynamic differential operator and its applications.

Inhalt

1 Introduction.- 2 Peridynamic Differential Operator.- 3 Numerical Implementation.- 4 Interpolation, Regression and Smoothing.- 5 Ordinary Differential Equations.- 6 Partial Differential Equations.- 7 Coupled Field Equations.- 8 Integro-Differential Equations.- 9 Weak Form of Peridynamics.- 10 Peridynamic Least Squares Minimization.